Physics Challenge for Boris Korsunsky, Column Editor Teachers … · 2019. 3. 7. · Diego...
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w Honorable discharge In the circuit shown, all capacitors are identical. Initially, the switch is open and the capacitor marked (*) is the only one charged. After the switch is closed and the equilibrium is reestablished, the charge on the capacitor marked (*) is Q. What was the initial charge Q 0 on that capacitor? Solution: We begin with the circuit given, assigning names to each identical capacitor. C 1 begins with an unknown initial charge Q 0 , and achieves a charge Q after the circuit is connected and has reestablished equilibrium. As C 3 is clearly shorted, the potential difference across its plates is 0, and as such the capacitor will contain no charge and will not affect the circuit. We can therefore remove it from the schematic. This simplified circuit can be broken down into even simpler equivalent circuits. Leaving C 1 where it is, and Physics Challenge for Teachers and Students Boris Korsunsky, Column Editor Weston High School, Weston, MA 02493 [email protected] Solutions to March 2012 Challenge THE PHYSICS TEACHER ◆ Vol. 50, 2012 recognizing C 5 and C 6 in series with each other (yield- ing an equivalent capacitance of 1/2C), and together in parallel with C 4 yields: Acknowledging the combined capacitors are equal, C 456 must have an equivalent capacitance of 3/2C. As C 456 is simply in series with C 2 , the resultant equivalent circuit has simply one capacitor (C 2456 ) in series with C 1 , where C 2456 must have an equivalent capacitance of 3/5C. Since Q = CV, V 1 = Q/C V 2456 = 5Q’/3C, where V 1 is the potential difference across C 1 , V 2456 is the potential difference across C 2456 , and Q’ is the charge on C 2456 . For equilibrium conditions, V 1 = V 2 . Therefore, Q/C = 5Q’/C 3CQ = 5CQ’ Q’ = (3/5)Q. By the conservation of charge, Q 0 = Q + Q’ Q 0 = Q + (3/5)Q Q 0 = (8/5)Q. The initial charge on the capacitor was 8/5 of the final charge on the capacitor after the switch was closed. (Contributed by Shaun M. Workenaour, Jiangsu Tianyi High School, Wuxi, China) * C1 C4 C 2 C 3 C 6 C 5 C 1 C 2 C 4 C 5 C 6 C 1 C 456 C 2
Transcript of Physics Challenge for Boris Korsunsky, Column Editor Teachers … · 2019. 3. 7. · Diego...
w Honorable dischargeIn the circuit shown, all capacitors are identical. Initially, the switch is open and the capacitor marked (*) is the only one charged. After the switch is closed and the equilibrium is reestablished, the charge on the capacitor marked (*) is Q. What was the initial charge Q0 on that capacitor?
Solution: We begin with the circuit given, assigning names to each identical capacitor. C1 begins with an unknown initial charge Q0, and achieves a charge Q after the circuit is connected and has reestablished equilibrium.
As C3 is clearly shorted, the potential difference across its plates is 0, and as such the capacitor will contain no charge and will not affect the circuit. We can therefore remove it from the schematic.
This simplified circuit can be broken down into even simpler equivalent circuits. Leaving C1 where it is, and
Physics Challenge for Teachers and Students
Boris Korsunsky, Column EditorWeston High School, Weston, MA 02493 [email protected]
Solutions to March 2012 Challenge
The Physics Teacher ◆ Vol. 50, 2012
recognizing C5 and C6 in series with each other (yield-ing an equivalent capacitance of 1/2C), and together in parallel with C4 yields:
Acknowledging the combined capacitors are equal, C456 must have an equivalent capacitance of 3/2C. As C456 is simply in series with C2, the resultant equivalent circuit has simply one capacitor (C2456) in series with C1, where C2456 must have an equivalent capacitance of 3/5C.
Since Q = CV,V1 = Q/CV2456 = 5Q’/3C,
where V1 is the potential difference across C1, V2456 is the potential difference across C2456, and Q’ is the charge on C2456.
For equilibrium conditions, V1 = V2.Therefore,
Q/C = 5Q’/C3CQ = 5CQ’Q’ = (3/5)Q.
By the conservation of charge, Q0 = Q + Q’Q0 = Q + (3/5)QQ0 = (8/5)Q.
The initial charge on the capacitor was 8/5 of the final charge on the capacitor after the switch was closed.
(Contributed by Shaun M. Workenaour, Jiangsu Tianyi High School, Wuxi, China)
*
C1
C4
C2
C3C6
C5
C1
C2
C4
C5
C6
C1
C456
C2
We would also like to recognize the following contribu-tors:Sharmila Balamurugan (student, Women’s Christian Col-
lege, Chennai, India)Hratch Barsoumian (Haigazian University, Beirut,
Lebanon)Mark Brown (Cretin-Derham Hall H.S., St. Paul, MN)Phil Cahill (Phil Cahill (The SI Organization, Inc.,
Rosemont PA)Jaime Carrillo Moreno, student (Escuela Politécnica
Superior, Universidad de Sevilla, Sevilla, Spain)David A. Cornell (emeritus, Principia College, Elsah, IL)Juan Díaz Vergara, Instituto Hebreo, Santiago, ChileDon Easton (Lacombe, Alberta, Canada)Oscar Escucha García, student (Escuela Politécnica
Superior, Universidad de Sevilla, Sevilla,Fernando Ferreira (Universidade da Beira Interior,
Covilhã, Portugal) Ángel García Rivera, student (Escuela Politécnica Superior,
University of Seville, Seville, Spain)Alexandru Gherghel-Lascu (Physics College, University of
Bucharest)Francisco Javier Gómez Gómez, student (Escuela Politéc-
nica Superior, University of Seville, Seville, Spain)Norge Cruz Hernández (Universidad de Sevilla, Sevilla,
Spain) Dante Herrera Aguilera, student (Escuela Politécnica
Superior University of Seville, Seville, Spain)Gerald E. Hite (TAMUG, Galveston, TX)Charles Holbrow (Colgate University, Hamilton, NY)Art Hovey (retired, Milford, CT)José Ignacio Íñiguez de la Torre (Universidad de
Salamanca, Salamanca, Spain)Kenneth E. Jesse (emeritus, Illinois State University,
Normal, IL)David Jones (Florida International University, Mi-
ami, FLMike Malak (Hudson Valley Community College)Nicolás Mangas Trabajo(student, Escuela Politécni-
ca Superior University of Seville, Seville, Spain)Stephen McAndrew (Macquarie University, Sydney,
Australia) Daniel Mixson (Naval Academy Preparatory
School, Newport, RI)Carl E. Mungan (U. S. Naval Academy, Annapolis,
MD) Thomas Olsen (Society of Physics Students, AIP,
College Park, MD)Israel Pérez Luna (student, Escuela Politécnica Su-
perior, Universidad de Sevilla, Sevilla, Spain)Michael Rapport (Anne Arundel Community Col-
lege, Arnold, MD)Wolfgang Rueckner (Harvard University Science
Center, Cambridge, MA)Jim Schreve (Hamilton College, Clinton, NY)Jason L. Smith (Richland Community College,
Decatur, IL) Cássio dos Santos Sousa (student, Instituto
Tecnológico de Aeronáutica, São Paulo, Brazil) Clint Sprott (University of Wisconsin – Madison,
WI)Liviu Cristian Tănase (Physics College, University
of Bucharest)Diego Francisco Tejero Fernández (student, Es-
cuela Politécnica Superior, University of Seville, Seville, Spain)
Many thanks to all contributors and we hope to hear from you in the future!
